Problem: $\vec u = (-4,-12)$ $\vec w = (-3,5)$ $\vec u + \vec w= ($
Answer: We add vectors by adding corresponding components: $\begin{aligned} \vec u + \vec w &= (u_x, u_y) + (w_x, w_y) \\\\ &= (u_x+w_x, u_y+w_y) \end{aligned}$ $\begin{aligned} \vec u + \vec w &= (-4,-12) + (-3,5) \\\\ &= (-4+(-3),-12+5) \\\\ &= (-7,-7) \end{aligned}$ The answer: $ \vec u + \vec w = (-7,-7) $